1. Field of the Invention
The present invention relates to a pressure transducer, and more particularly a compact robust pressure transducer that can be included with a temperature output. The invention further relates to a compactly packaged pressure transducer that is well suited to measuring underwater pressures.
2. Description of the Prior Art
Real time acquisition of pressure and temperature data is essential for dynamic engine control and performance optimization of automotive, hydraulic, off-road vehicles, and marine systems. Underwater applications of the present invention include: passive depth finders (stand alone or complementary to sonar) for autonomous vehicles and their navigation, submarines, diving equipment, and off-shore drilling and exploration.
A brief discussion of material and device physics that leads to the present invention will be given. Piezoresistivity is the linear coupling between mechanical stress (pressure) and electrical resistivity. It has been observed in many solids. The specific change in resistivity ρij with stress σkl is given byΔρij/ρ(0)=ΣkΣlπijklσkl, (i, j, k, l=1, 2, 3)  (1)where ρ(0) is the zero-stress resistivity. The piezoresistivity tensor πijkl in Eq. (1) has the dimension of reciprocal stress (m2/N). Using the condensed subscript notation, Equation 1 could be written in terms of the conjugate strain εk as followsΔρi/ρ(0)=Σjπijσj=ΣjΣkπijcjkεk=Σkmikεk, (i, j, . . . =1, 2, 3, . . . 6)  (2)where, mik=Σj πij cjk. The dimensionless mik is the elastoresistance tensor known as the gauge factor. The three independent πij coefficients for silicon (cubic symmetry group m3m) are π11, π12, and π44. The hydrostatic coefficient is given by πh=−(π11+2π12). For isotropic (spherical symmetry group ∞/∞ mm) solids, there are only two independent components π11 and π12 with π44=2(π11−π12) and πh=−(π11+2π12). The longitudinal, transverse, and shear modes in silicon have been used in many commercial pressure, vibration, acceleration, strain, and tactile sensors. Elastic effects, i.e., resistance change due to changes in dimension of the piezoresistor with mechanical stress must be factored out, in order to obtain the true piezoresistive effect. In other words, the experimentally derived piezoresistance coefficients Πij=(1/Ro) (∂Ri/∂σj), where Ro and Ri are the unstressed and stressed resistances respectively, must be corrected for elasticity to obtain the true piezoresistivity πij coefficients. The corrections for the longitudinal Π11, transverse Π12, and hydrostatic Πh components are given by,π11=Π11−(s11−2s12)  (4)π12=Π12+s11.  (5)=πh=Πh−(s11+2s12)  (6)where Πh=(1/Ro) (∂R1/∂σh) is the experimentally derived hydrostatic piezoresistance coefficient and sij are the elastic compliances that appear in the linear theory of elasticity. For screen printed metal-insulator-metal (MIM) structures, the elastic compliances sij are those of the substrate.
Numerical values for silicon and commercial Electro-Science Laboratories (ESL) ruthenium based MIM piezoresistors are listed in Table I. Note the large hydrostatic piezoresistivity coefficient πh of MIM structures relative to those of silicon, in addition to a much lower temperature coefficient of πh˜430 ppm/° C. for MIM piezoresistors as opposed to 2000 ppm/° C. for silicon. The two engineering parameters for a transducer design, namely, the magnitude and temperature dependence of πh (span) and the direct current resistance at zero stress (offset) for a ruthenium-based MIM structure are known in the art.
ResistivityMaterial(Ω-cm)π11π12π44π1πhn-Si11.7−1022530116−102238p-Si 7.866−111383935−44ESL D3414 4 (kΩ)45a30a−310aESL 3414A 8 (kΩ)−4.90aaRoom temperature values), the temperature coefficient of πij is ~2000 ppm/° C. for Si and ~430 ppm/° C. for ESL MIM piezoresistors.
Table I. Piezoresistivity Coefficients πij (10−12 m2/N)
As seen from Table I, the hydrostatic coefficient for silicon, is rather small compared to the longitudinal, transverse and shear components. However, the converse is true for ruthenium based MIM structures. The hydrostatic coefficient πh is approximately ten times that of the other two coefficients. Besides, it is much higher than what would be expected from the relationship πh=−(π11+2π12) assuming a spherical symmetry. Theoretical interpretation of this phenomenon is given in A. Amin, Piezoresistivity of Ruthenium-Based-Metal-Insulator-Metal Structures, J. Mat. Res. 16 (8), 2239–2243 (2001) which is incorporated herein by reference.
The longitudinal piezoresistivity coefficient π1 and maximum sensitivity directions for silicon can be determined from the symmetry allowed π11, π12, and π44 coefficients. For a thin long bar cut parallel to an arbitrary direction in the crystal, π1 is given by,π1=π11+2(π44+π12−π11)F(θ,φ),  (7)where F(θ,φ)=sin2θ cos2θ+cos4θ cos2φ sin2φ. According to Eq. (7), sensitivity extrema are along the 4-fold symmetry directions for n-type silicon and the 3-fold symmetry directions for p-type. This representation illustrates the need for precise alignment of the maximum sensitivity directions of silicon piezoresistors along the stress maxima on the diaphragm. This requirement becomes inconsequential under hydrostatic pressure, the representation surface degenerates to a sphere with radius vector equal to πh. The magnitude of πh is rather small for silicon, in comparison to the recently discovered ruthenium-based MIM structures. (See Table I).
The most common geometry of piezoresistive pressure sensors is the edge clamped diaphragm. Four resistors are usually deposited on the diaphragm and connected to form a Wheatstone bridge. The resistors are oriented in a manner to take advantage of the maximum sensitivity directions of the piezoresistive element as described by Eq. (7) and the elastic boundaries in the diaphragm to double the bridge response to pressure signals. To design an accurate and sensitive sensor, it is necessary to analyze the diaphragm stress-strain response using plate theory and finite element techniques. Elastic anisotropy, nonlinearity, and maximum piezoresistivity directions must all be considered in the analysis. The deposition technique and complexity are application specific. They depend on the piezoresistor and diaphragm materials. Standard integrated circuit (IC) technology and micromachining are used for fabricating silicon pressure sensors. For hybrid devices, sputtering is used for thin metallic films and screen-printing for thick films, respectively. The diaphragm material ranges from Si and Ge to alumina, sapphire, and dielectric coated stainless steel.
The problems associated with micro-machined piezoresistive silicon and other diaphragm-type architecture are thermal drift errors, response nonlinearity, and hysteresis. Besides, media compatibility has been problematic for the silicon diaphragm pressure sensor. A temperature change can cause the sensor's offset and span (sensitivity) to vary independently, giving rise to an undesired output. Minor process variations, e.g., resistor misalignment, variations in the diaphragm thickness and anisotropy of the elastic properties, will contribute to response nonlinearity and hysteresis. Two orthogonal calibrations are required to eliminate thermal errors in offset and span. Application specific temperature compensation techniques using laser trimming and external resistors have been employed for limited pressure and temperature ranges. Simulation techniques to analyze the effect of error sources on the sensor output and to provide digital compensation algorithms using integrated circuit technology are available.